Fox News Channel chairman and CEO Roger Ailes has been adamant that network anchor Megyn Kelly will remain as moderator of Thursday's scheduled Republican presidential debate on the network -- even as GOP front-runner Donald Trump has pushed back against the decision.

Trump on Tuesday gave Ailes an ultimatum: Either Kelly's out as moderator, or he walks.

"We learned from a secret back channel that the Ayatollah and Putin both intend to treat Donald Trump unfairly when they meet with him if he becomes president — a nefarious source tells us that Trump has his own secret plan to replace the Cabinet with his Twitter followers to see if he should even go to those meetings," the Fox statement said, CNN Money reported.

There has been ill will between Trump and Kelly since the first Republican debate in August, when the businessman denounced Kelly's line of questioning as unfair.

“Megyn Kelly’s really biased against me,” Trump says in an Instagram video posted Tuesday. “She knows that. I know that. Everybody knows that. Do you really think that she can be fair at a debate?”

If Trump walks, the network could risk losing viewership. The businessman has claimed full responsibility for Fox News' highest ratings in 20 years at the August debate. More than 24 million people tuned into watch Trump spar with the other Republican candidates.

.@FoxNews you should be ashamed of yourself. I got you the highest debate ratings in your history &amp; you say nothing but bad...